, Volume 3, Issue 3, pp 371-397

Construct irreducible representations of quantum groups U q (ƒ m (K))

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Abstract

In this paper, we construct families of irreducible representations for a class of quantum groups U q (ƒ m (K)). First, we give a natural construction of irreducible weight representations for U q (ƒ m (K)) using methods in spectral theory developed by Rosenberg. Second, we study the Whittaker model for the center of U q (ƒ m (K)). As a result, the structure of Whittaker representations is determined, and all irreducible Whittaker representations are explicitly constructed. Finally, we prove that the annihilator of a Whittaker representation is centrally generated.